A336369 Primes p(n) such that gcd(n, prime(n)+prime(n+1)) > 1.

3, 5, 7, 13, 19, 29, 37, 43, 47, 53, 61, 71, 79, 89, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 173, 181, 193, 197, 199, 223, 229, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 397, 409, 419, 421, 433

Offset: 1

Author

Clark Kimberling, Oct 04 2020

Keywords

• nonn

Comments

This sequence and A336368 partition the set of primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n+1)   gcd
  1     2         5          1
  2     3         8          4
  3     5        12          3
  4     7        18          2
  5    11        24          1
  6    13        30          6
1 and 5 are in A336366; 2 and 3 are in A336367; 2 and 11 are in A336368; 3 and 5 are in A336369.
		

Crossrefs

Cf. A000040, A336366, A336367, A336368.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &]  (* A336366 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &]   (* A336367 *)
Prime[u] (* A336368 *)
Prime[v] (* A336369 *)